Mathematics MCQs

Mathematics ? Vector Calculus Questions with solutions MCQs

1. Gradient properties: If f scalar, C constant. Match: i. ?(Cf) ii. ?(u+v) iii. ???f. Answers: (1) C?f, (2) ?u+?v, (3) ??f.

A

(i)-2, (ii)-3, (iii)-1

B

(i)-3, (ii)-2, (iii)-1

C

(i)-1, (ii)-2, (iii)-3

D

None

Mathematics ? Vector Calculus J.E Civil (SD) 2025
Correct Answer : C
Explanation :

?(Cf)=C?f, ?(u+v)=?u+?v, ???f=??f.

Correct Answered :

Wrong Answered :

2. Stokes theorem valid irrespective of: 1. Shape of closed curve C 2. Type of vector A 3. Type of coordinate system 4. Surface closed/open. Which correct?

A

1,2,4

B

1,3,4

C

1,2,3

D

1,2,3,4

Mathematics ? Vector Calculus J.E Civil (SD) 2025
Correct Answer : C
Explanation :

Stokes theorem is independent of shape of curve, vector type, and coordinates.

Correct Answered :

Wrong Answered :

3. Stokes theorem and Green?s theorem: 1. Green?s is particular case of Stokes. 2. Stokes is particular case of Green?s. 3. Both same. Choose correct.

A

1 correct, 2&3 incorrect

B

2 correct, 1&3 incorrect

C

3 correct, 1&2 incorrect

D

1,2,3 incorrect

Mathematics ? Vector Calculus J.E Civil (SD) 2025
Correct Answer : A
Explanation :

Green?s theorem is indeed a special case of Stokes theorem in 2D.

Correct Answered :

Wrong Answered :

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